When potential workers apply for a job that requires extensive manual assembly of small intricate parts, they are initially given three different tests to measure their manual dexterity. The ones who are hired are then periodically given a performance rating on a 0 to 100 scale that combines their speed and accuracy in performing the required assembly operations. The file P14_36.xlsx lists the test scores and performance ratings for a randomly selected group of employees. It also lists their seniority (months with the company) at the time of the performance rating.

a. Run the regression of Performance Rating versus all four explanatory variables. List the equation, the R-square value, and the standard error of estimate. Do all of the regression coefficients have the signs you would expect? Briefly explain.

b. Referring to the equation in part a, if a worker (out-side of the 80 in the sample) has 15 months of seniority and test scores of 57, 71, and 63, give a prediction and an approximate 95% prediction interval for this worker’s Performance Rating score.

c. Arguably, the three test measures provide overlapping (redundant) information. It might be sensible to regress Performance Rating versus only two explanatory variables, Seniority and Average Test, where Average Test is the average of the three test scores, that is, Average Test = (Test1 + Test2 + Test3)/3. Run this regression and report the same measures as in part a: the equation itself, R-square, and the standard error of estimate. Can you argue that this equation is just as good as the equation in part a? Explain briefly.